System Identification for the Hodgkin-Huxley Model using Artificial Neural Networks

Abstract

A single biological neuron is able to perform complex computations that are highly nonlinear in nature, adaptive, and superior to the perceptron model. A neuron is essentially a nonlinear dynamical system. Its state depends on the interactions among its previous states, its intrinsic properties, and the synaptic input it receives. These factors are included in Hodgkin-Huxley (HH) model, which describes the ionic mechanisms involved in the generation of an action potential. This paper proposes training of an artificial neural network to identify and model the physiological properties of a biological neuron, and mimic its input-output mapping. An HH simulator was implemented to generate the training data. The proposed model was able to mimic and predict the dynamic behavior of the HH simulator under novel stimulation conditions; hence, it can be used to extract the dynamics (in vivo or in vitro) of a neuron without any prior knowledge of its physiology. Such a model can in turn be used as a tool for controlling a neuron in order to study its dynamics for further analysis.

Methodology of Recurrent Laguerre–Volterra Network for Modeling Nonlinear Dynamic Systems

“…The recent development of a stochastic H-H model is trying to capture some of these variabilities by introducing noise terms in the deterministic H-H equations [41–46]. On the other hand, the data-based non-parametric methods, such as nonlinear autoregressive Volterra (NARV) modeling [5], conventional PDM analysis [6], and recurrent ANN [47] have been utilized to approximate the AP generation process. These non-parametric methods, however, cannot provide biological insights through interpretation of the obtained models.…”

Kalman filter tracking of intracellular neuronal voltage and current

“…The response of a single neuron is complex and depends on the interactions between its previous state, its intrinsic properties, and the external stimuli or synaptic currents it receives [2]. Although we can measure single neuron properties via patch clamp techniques, the underlying input current and neural dynamics are not directly measurable.…”

“…Computational models have been increasingly used as an alternative to tackle these challenges that are encountered in such experiments. Previous studies on the input-output relationship of a neuron have been carried out by conventional filters [4], artificial neural networks [2], and a numerical model [3]. These approaches are helpful to establish a quantitative relationship between neuron response and input stimulus.…”

Attack of Against Simplified Data Encryption Standard Cipher System Using Neural Networks

“…The first approach is the State-Space approach (internal description), which describes the internal state of the system and is used whenever the system dynamical equations are available. The second approach is the Black-Box approach (input-output description) which is used when no information is available about the system except its input and output (Saggar et al, 2007). Figure 1 shows an unknown system with x m input signals and y n output signals.…”

“…Clearly what one can do to a black box, is to apply inputs and measure their corresponding outputs and then try to abstract key properties of the system from these input-output pairs. An input-output model assumes that the new system output can be predicted by the past inputs and outputs of the system (Saggar et al, 2007;Liu and Truong, 1995). A Black-Box model of system identification assumes no prior knowledge about the system except it's input and output, i.e., no matter what analysis is used, it always lead to the same input-output description.…”